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where \( Re \) is the Reynolds number. However, as the flow transitions to a turbulent regime, the calculation becomes more complex. The turbulent flow friction factor is determined using empirical correlations, such as the Colebrook-White equation, which accounts for both the Reynolds number and the relative roughness of the pipe.
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In recent years, the pharmaceutical industry has faced significant challenges regarding the availability and quality of raw materials. Factors such as geopolitical tensions, trade restrictions, and the COVID-19 pandemic have disrupted supply chains, leading to shortages of essential APIs and raw materials. This situation has spotlighted the need for greater resilience and diversification of supply sources. Companies are now encouraged to consider multiple suppliers and invest in local sourcing to mitigate risks associated with disruptions.
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